Mathematics of FinanceMCQMTP Nov 21Question 1334 of 512
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He effective rate of interest equivalent to the nominal rate of 7%\displaystyle 7\% converted monthly:

Options

A7.26%\displaystyle 7.26\%
B7.22%\displaystyle 7.22\%
C7.02%\displaystyle 7.02\%
D7.20%\displaystyle 7.20\%
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Correct Answer

Option b7.22%\displaystyle 7.22\%

All Options:

  • A7.26%\displaystyle 7.26\%
  • B7.22%\displaystyle 7.22\%
  • C7.02%\displaystyle 7.02\%
  • D7.20%\displaystyle 7.20\%

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Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal interest rate (r\displaystyle r) = 7%\displaystyle 7\% per annum - Compounding Frequency = Converted monthly (m=12\displaystyle m = 12) **Step 1: Find the monthly interest rate (i\displaystyle i)** i=rm=7%120.5833%=0.005833 per monthi = \frac{r}{m} = \frac{7\%}{12} \approx 0.5833\% = 0.005833 \text{ per month} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m1E = (1 + i)^m - 1 E=(1+0.005833)121E = (1 + 0.005833)^{12} - 1 E=(1.005833)121E = (1.005833)^{12} - 1 E1.072291=0.07229 or 7.22%E \approx 1.07229 - 1 = 0.07229 \text{ or } 7.22\% Hence, **Option B** is the correct answer.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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